The sharp upper bounds and the sharp lower bounds of the largest eigenvalues $\lambda_1$, the least eigenvalue $\lambda_n$, the second largest eigenvalue $\lambda_2$, the spread and the separator among all firefly graphs on $n$ vertices are determined.
J. A. Bondy and U. S. R. Murty (1976). Graph Theory with Applications. American Elsevier Publishing Co., Inc., New York. F. K. Bell, D. Cvetkovic, P. Rowlinson and S. K. Simic (2008). Graphs for which the least eigenvalue is minimal, I. Linear Algebra Appl.. 429, 234-241 F. K. Bell, D. Cvetkovic, P. Rowlinson and S. K. Simic (2008). Graphs for which the least eigenvalue is minimal, II. Linear Algebra Appl.. 429, 2168-2179 D. Cvetkovic and S. Simic (1995). On graphs whose second largest eigenvalue does not exceed $\frac{\sqrt{5}-1}{2}$. Discrete Math.. 138, 213-227 D. Cvetkovic and P. Rowlinson (1990). The largest eigenvalue of a graph: a survey. Linear and Multilinear Algebra. 28, 3-33 D. Cvetkovic, P. Rowlinson and S. Simic (2010). An Introduction to the Theory of Graph Spectra. Cambridge University Press, Cambridge. 75 Y. Fan, Y. Wang and Y. Gao (2008). Minimizing the least eigenvalues of
unicyclic graphs with application to spectral spread. Linear Algebra Appl.. 429, 577-588 Y. Hong Bounds on the spectra of unicyclic graphs. (Chinese), J. East China Norm. Univ. Natur. Sci. Ed.. 1986 (1), 31-34 J. X. Li, J. M. Guo and W. C. Shiu (2013). On the second largest Laplacian eigenvalues of graphs. Linear Algebra Appl.. 438, 2438-2446 S. C. Li and M. J. Zhang (2012). On the signless Laplacian index of cacti with a given number of pendant vertices. Linear Algebra Appl.. 436, 4400-4411 Q. Li and K. Feng (1979). On the largest eigenvalues of a graphs. (Chinese), Acta Math. Appl. Sinica. 2, 167-175 M. Petrovic, T. Aleksic and V. Simic (2011). On the least
eigenvalue of cacti. Linear Algebra Appl.. 435, 2357-2364 B. Wu, E. Xiao and Y. Hong (2005). The spectral radius of trees on k pendant vertices. Linear Algebra Appl.. 395, 343-349 G. H. Xu (2004). On unicyclic graphs whose second largest eigenvalue does not exceed 1. Discrete Appl. Math.. 136, 117-124
)
